How do you solve $5 /( y-2) = y+2$ and find any extraneous solutions?

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Answer 1 · 2016-06-12T19:35:05

First, let us identify any restrictions on the variable.

In rational equations, restrictions make the denominator be equal to $0$ .

Therefore, we can find any restrictions by setting the denominator to 0 and solving.

$y - 2= 0$

$y = 2$

Thus, $y !=2$ .

Solving:

$5 = (y + 2)(y - 2)$

$5 = y^2 - 4$

$9 = y^2$

$+-3 = y$

Neither of these contradict the restrictions, therefore our solution set is ${y = +-3}$ .

Hopefully this helps!

How do you solve 5 /( y-2) = y+2 5 /( y-2) = y+2 and find any extraneous solutions?